Hull City missed the chance to go fifth as three goals in the final 12 minutes gave Burnley all three points on Saturday afternoon.
The away side missed a golden chance to take the lead inside the opening minute when Jay Rodriguez advanced on goal, but Jack Hobbs's saving tackle prevented him from getting a shot away.
The home side took the lead in the 11th minute however, with a well-taken goal from Matt Fryatt after good play from Cameron Stewart.
Hull took control of proceedings from that moment on and found themselves 2-0 ahead after 55 minutes when Fryatt grabbed his second of the afternoon from just inside the area.
Burnley were struggling as the second half progressed but found themselves back in the game after 78 minutes when David Edgar headed in from a corner.
It was Edgar once more who brought the score level at 2-2 three minutes later when he drilled home from close range after good work from Kieran Trippier.
Hull stemmed the onslaught and had seemed certain to settle for a point in the latter stages but Burnley had other ideas and found a winner in the third minute of additional time.
Chris McCann found Jay Rodriguez, who coolly slotted the ball into the bottom left-hand corner to secure all three points for Burnley on a dramatic afternoon.
Burnley rise to 16th with the win, while Hull remain a spot outside the play-offs.
